### The Maxima on-line user's manual

Algebra Calculator

#### Pochhammer

Function: pochhammer (<n>, <x>) The Pochhammer symbol. For nonnegative integers <n> with `<n> <= pochhammer_max_index`, the expression `pochhammer (<x>, <n>)` evaluates to the product `<x> (<x> + 1) (<x> + 2) ... (<x> + n - 1)` when `<n> > 0` and to 1 when `<n> = 0`. For negative <n>, `pochhammer (<x>, <n>)` is defined as `(-1)^<n> / pochhammer (1 - <x>, -<n>)`. Thus

```          (%i1) pochhammer (x, 3);
(%o1)                   x (x + 1) (x + 2)
(%i2) pochhammer (x, -3);
1
(%o2)               - -----------------------
(1 - x) (2 - x) (3 - x)```

To convert a Pochhammer symbol into a quotient of gamma functions, (see Abramowitz and Stegun, equation 6.1.22) use `makegamma`; for example

```          (%i1) makegamma (pochhammer (x, n));
gamma(x + n)
(%o1)                     ------------
gamma(x)```

When <n> exceeds `pochhammer_max_index` or when <n> is symbolic, `pochhammer` returns a noun form.

```          (%i1) pochhammer (x, n);
(%o1)                         (x)
n```

There are also some inexact matches for `pochhammer`. Try `?? pochhammer` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### pochhammer

pochhammer (2/3, 2);

pochhammer (2/3, 3);

pochhammer (2/3, 4);

Calculate

##### pochhammer

pochhammer ( 3/2,3);

Calculate

##### pochhammer

pochhammer (3, 4);

Calculate

##### pochhammer

pochhammer (-2,0);

Calculate

##### pochhammer

pochhammer (5, 2);

fibonacci(4);

Calculate

##### pochhammer

pochhammer (3, 2);

Calculate

##### pochhammer

pochhammer (3, 5);

Calculate

##### pochhammer

pochhammer (4,3 );

Calculate

##### pochhammer

pochhammer (4, 1);

Calculate

##### pochhammer

pochhammer (5,0 );

Calculate